phpBB
mySQL
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That should get you started, though you will have to have some sort of hosting service that supports SQL and PHP. Most cost, but not much at all (I think I once found hosting for $4.95/month).

If that's all over your head, then there's not much else you can do except put up with Invision or pay a lot of vB. Oh, also if you don't know how to make forum layouts, you can usually find templates for phpBB that you can modify.

I know a fair few people will be able to help more than I can though.